1. ## coin flipped

the probability of getting a head on flipping a biased coin is p. the coin is flipped n times producing a sequence containing m heads and (n-m) tails what is the probability of obtaining this sequence from n flips.
i cant understand the wording

2. ## Re: coin flipped

You have a biased coin with probability of flipping heads = $p$

You flip this coin $n$ times

what is the probability you flip $m$ heads

Is it P(n)^m

Is it P(n)^m

5. ## Re: coin flipped

Have you studied the binomial distribution yet?

yes

7. ## Re: coin flipped

Originally Posted by markosheehan
yes
Ok. So you should be familiar with the formula:

$P(X=r) = nCr*p^r*q^{n-r}$

So, what is n, r, p and q in this case?

8. ## Re: coin flipped

when i put this all together i get (n ncr m)*p*(1-p)^n-m however at the back of the book it says the answer is p^m(1-p)^n-m

9. ## Re: coin flipped

Originally Posted by markosheehan
when i put this all together i get (n ncr m)*p*(1-p)^n-m however at the back of the book it says the answer is p^m(1-p)^n-m

Going back to the question "the coin is flipped n times producing a sequence containing m heads and (n-m) tails". If this means "m heads and then (n-m) tails",
the answer in your book is correct. The nCm multiplier accounts for all the ways you can get m heads and (n-m) tails , ie in any order.

I would interpret "a sequence containing m heads and (n-m) tails" as meaning "in any order" eg HHHTT, HTHTH, THHHT all need to be accounted for.